Política pública: una clarificación conceptual

computedM_HI/Area26.5quantities. As shown in the plot, most data points for the dwarf galaxies are scattered around unity typically by within 0.5 dex. There is an obvious trend from overestimation to underestimation with increasing H i mass. Fortunately this bias appears to be linear and we correct for it using a least squares (solid line Fig.4.5) approach. The correlation coefficient of this fit is r = 0.750 . We derive the following correction for the dwarf galaxies,ΣHI=(0.4 ± 0.1)MHI/Area26.5 + (0.38 ± 0.04), which is applied before correcting for Helium.

Fig.4.5illustrates a high degree of scatter from our proxy and theKennicutt(1998) surface averaged method. Some of this is attributable to the more modern values we used in our calculation. Another significant contributor is that our parameter only accounts for the H i gas and not the total gas and so we would expect our proxy to underestimate the surface density relative to theKennicutt(1998) sample. Fig.4.5instead demonstrates the opposite trend, with our proxy over-estimating theKennicutt(1998) sample. The implication is that choice in radius is significant for the spiral galaxies, and a more robust measure of the size of the galaxy is required for large spirals whose morphology and optical to H i diameters can vary significantly relative to the dwarf galaxies (seeKoribalski et al.(2018) for typical optical HI diameters for LV dwarfs).

Given that dwarf galaxies will remain unresolved for the foreseeable future, this method is the only way to compare dwarfs to spirals in statistically meaningful samples and it is therefore fortunate that the scatter for dwarf galaxies in Fig. 4.5is within an order of magnitude and the bias is linear.

4.5.

The Kennicutt-Schmidt relation for Local Volume galaxies

Using the data and derived parameters described in Section2.3, we plot the gas and SFR surface densities. Figure4.6explores the simple linear regression to the SFR relation for

low surface brightness galaxies fromKJRD08,YJLK14andMVPB12. Figure4.7extends

the regression analysis to include low surface brightness galaxies and spiral galaxies from further sources (Roychowdhury et al. 2014;Wyder et al. 2009;Kennicutt 1998) while the outer disk (Bigiel et al. 2010) and starburst data (Kennicutt 1998) is included in the plot for comparative purposes only. For the low surface brightness galaxies fromKJRD08,YJLK14

andMVPB12, the best fitting relation resulting from the least squares regression to the data

in Fig.4.6was found to be,

log₁₀ΣSFR,LSB=2.4−+00..33log10ΣHI−4.8+−00..22 (4.1) whereΣHIis the surface density of the H i gas andΣSFR,LSBis the star formation rate surface density in low surface brightness galaxies. Including data fromRoychowdhury et al.(2014),

Wyder et al.(2009) andKennicutt(1998) the corresponding best fitting relation to the data

in Fig.4.7is instead,

log₁₀ΣSFR=2.2+−00..11log10Σgas−4.8+−00..22 (4.2) As shown in Fig. 4.6, there is a clear correlation between the surface densities of the SFR and the atomic gas with a steep dependence on the latter quantity. Although we did not include

-5 -4 -3 -2 -1 log 10 ΣSFR [ M sol yr -1 Kpc -2 ] 2.5 2.0 1.5 1.0 0.5 0.0 -0.5

log10Σgas [ Msol pc -2

]

1010

1011 109

Figure 4.6 The simple linear regression to the low surface brightness galaxies obtained from the NIR samples,

KJRD08, YJLK14and MVPB12and whose atomic gas surface densities have been estimated from global

parameters as outlined in Section3.2. Dashed lines corresponds to slopes of constant gas depletion times in units of years. The solid black line corresponds to the fitted linear regression (correlation coefficient r = 0.670).

theBigiel et al.(2010) data in the least squares fit shown in Fig.4.7, visual comparison of

their data set to the line of best fit shows good agreement. The slopes derived for the LSB galaxies in this study are much steeper than that found inRoychowdhury et al.(2014) and is more supportive of the findings ofRoychowdhury et al.(2015). Roychowdhury et al.(2015) suggested this difference could be an effect of being biased towards the inner star-forming regions of galaxies. If that were the case, we might expect the same phenomenon in our sample galaxies which are also disk averaged quantities. Instead they form a tight distribu- tion intermediate to the outer disk data ofBigiel et al.(2010) and the spirals ofKennicutt (1998). Our sample includes galaxies over a much wider range of surface brightness than the sample ofRoychowdhury et al.(2014): low surface brightness galaxies fromYJLK14, the somewhat brighter low-mass late types and irregulars fromKJRD08, as well as star-forming

dwarfs and additional low surface brightness galaxies from the amalgamatedMVPB12

sample. We suggest that N=1 (where N is a parameter in the equation of the form given in Eq. 1.1) slope found inRoychowdhury et al.(2014) could be simply due to insufficient statistics, especially given the generally good agreement between the combinedRoychow-

dhury et al.(2014),Wyder et al.(2009)KJRD08,YJLK14andMVPB12datasets. For dwarf

galaxies, we find a slope that is strictly not in agreement with the canonical N=1.4 derived from the originalKennicutt(1998) sample. AsBigiel et al.(2008) noted, the N=1.4 relies on the contrast of spiral disks and the molecular rich circumnuclear starbursts.

Notably, the galaxy NGC 1569 (labeled in Fig.4.7) lies well outside the expected behavior for spirals or dwarf galaxies. Environmental interactions resulting in the starburst activity are very likely to be the cause of NGC 1569 significant offset from the star formation relation

4.5 The Kennicutt-Schmidt relation for Local Volume galaxies 55 -5 -4 -3 -2 -1 0 1 log 10 ΣSFR [ M sol yr -1 Kpc -2 ] 3 2 1 0 -1

log10ΣGas [ Msol pc -2 ] Starbursts (K98) Spirals (K98) LSB (W09, R14) LSB (YJLK14, MVPB12, KRDJ08) 108 1010 109 1011 1012 NGC1569

Figure 4.7 The Kennicutt-Schmidt relation forYJLK14,MVPB12andKJRD08(open circles) sample galaxies compared to the originalKennicutt(1998) data (plus symbolsfor spirals,crossesfor starbursts). Additionally, we

have included the disk averaged quantities for the galaxies whose column densities were measured directly,

(Roychowdhury et al. 2014;Wyder et al. 2009,black triangles). The greyscale smoothed distribution represents

the outer disk data of H i -dominated dwarf and spirals galaxies fromBigiel et al.(2010). TheKennicutt(1998) galaxies have been corrected for the presence of helium contrary to the original work. The diagonal dashed lines corresponds to slopes of constant gas depletion times in units of years. The solid line is the line of best fit to selected data as described in the text (correlation coefficient r = 0.795).